James Weatherall's The Physics of Wall Streetclaims that you cannot drive over the George Washington Bridge without trusting mathematical modelers. This confused conclusion relates to his misunderstanding of Black Swans.

Nassim Taleb labeled extreme events that happen because they are unexpected "Black Swans," and argued that long-term results are dominated by them. Attempts to predict them or protect against them may make them less common, but only at the expense of making them bigger and more anomalous. There is quite a lot of theory and evidence to support this contention; it is not a midnight musing backed by a few anecdotes.

After disasters, people like Weatherall rush in to explain why the event should have been predicted, and to propose fixes. It usually turns out that people had already been taking more sophisticated precautions than the newcomers recommend, and in any case, more precautions may make the situation worse.

Weatherall appears to have read a review of Taleb's The Black Swan and missed the part of the definition about events happening because they are unexpected. People who never predict are never surprised. People who make simple, robust predictions and don't bet too much on them avoid extreme exposure to surprises. It takes sophisticated, fragile predictions that compile long-term track records of success and encourage excessive reliance to generate Black Swans. Black Swans do not come from nature; they are an unintended product of human engineering. Another key point Weatherall apparently misunderstands is that Black Swanness is not a property of an event -- it is a relation of an event to a person. The 9/11 attacks were not a Black Swan to the hijackers; it had extreme impact, but they expected it. It was not a Black Swan to most of the people in the world. They did not expect it, but it did not have an extreme impact on them. It was a Black Swan to US policymakers and many other groups, but not to everyone.

Because Weatherall thinks Black Swans are merely high-impact unusual events, he thinks he has a solution for them, which somehow eluded Nassim plus the millions of people who have bought his books. He says we must all think like physicists and anticipate the events, keeping in mind that we cannot anticipate perfectly. He claims that throwing out mathematical modeling is like refusing to drive over the George Washington Bridge.

Of course, that's a foolish point that is demolished thoroughly in Nassim's books. It takes real arrogance for Weatherall to think he is the first person to think of it, and that he can promote his rebuttal without having read The Black Swan. People do not drive over the George Washington Bridge because they understand the mathematical modeling underlying its design, but because it has carried people safely for 82 years. It may collapse someday, but the chance of it happening during your trip has to be pretty small. Moreover the bridge incorporates empirical insights from millennia of bridge building, plus fields like steel and concrete manufacture, civil engineering, and road safety. The chance of being killed in any manner by any sort of bridge is on the order of one in a million, and the overwhelming majority of that is the chance of deliberately jumping off one to kill yourself. Weatherall's contention echoes the point I made earlier that he views triumphs of engineering as illustrations of physical principles, and credits physicists for the work done by everyone else.

It's worth pausing for a moment to consider the role mathematical modeling plays in bridge design because it has some similarities to mathematical modeling in finance -- in fact, in most applied fields. Abstract mathematics may or may not play some part in the original conceptual design, but the many millions of calculations that went into the George Washington Bridge were mainly interpolations, or more daringly, extrapolations, from historical experience. We had data on the strength of single-strand steel cables, and also on the forces acting on bridges. None of this came from first principles of physics; it's too complicated to compute with enough accuracy for practical application. Mathematics - arithmetic, not advanced theoretical mathematics - is useful for scaling observed data to theoretical designs. While engineers do use concepts and formulae from physics, they could about an equally accurate job using simple assumptions and rules of thumb. Moreover, although calculations are done precisely, no one trusts them much, so large safety factors are routinely used to adjust the results. More recently, people have build computer simulations of structures, but these are calibrated to data, not based on theory. They're used for extreme stress testing and the results are merely suggestive; no one takes them seriously as predictions.

Physicists sometimes do something grander. They build an entirely new thing based on extensive theoretical calculation - an atomic bomb, a collider, a superconductor. These do involve real mathematics. But the practical implementation still takes a huge amount of arithmetic, trial and error, and scaling up of pilot implementations. Lots of engineers, technicians, machinists, and other skilled staff are necessary; these things do not spring directly from design to device.

Nassim's criticism of mathematical modeling refers to using pure theory to design something new, and putting it into practice without the hard work described in the last paragraph - and his point applies to all theory, whether or not it uses mathematics. No one disputes the value of arithmetic in building the George Washington Bridge, nor the insight mathematics can give a theoretical physicist. Weatherall cannot have thought much about these issues to think he needs to defend these uses of mathematics. What is under attack is the idea that insight alone is enough to make practical devices or systems.

One important difference between bridge building and mathematical modeling is that builders have skin the game. They must persuade people to trust them with resources to build, not to mention with the lives of bridge travelers. It will be obvious if they are not highly competent, because the bridge will not be built successfully in the first place. Engineers with extensive empirical experience will review every aspect of the planning and execution against history and the state of the art. Bridges still collapse, but not as often as they would if anyone could declare herself a bridge builder, without persuading anyone of anything, without any proof of competence, without any review and without any requirement to tie the model to empirical evidence. I'll bet even Weatherall is not arrogant enough to write The Physics of Bridge Building without any training, experience, or research in the field. He'd be afraid someone would take him seriously and people would get killed. But his physics PhD qualifies him in his mind to write books on mathematical reasoning in any field where practitioners are unlikely to take him seriously.

Just because mathematical modeling can be abused more easily than bridge building doesn't mean that it always is abused. Modelers can put skin in the game and bet meaningful personal stakes on their calculations. They can prove their competence, and ground their work thoroughly in empirical reality. They can incorporate safety factors set by experience, as bridge engineers do, doing a calculation and then tripling the result (or making some other adjustment) for safety. There could be standards for modeling and vigorous challenges in reviews. I think this is more or less what Weatherall advocates, anyway any reasonable person should support them. When these things are done, I believe even Nassim would trust the model to a limited extent, just as he drives over the George Washington Bridge without necessarily predicting it will never collapse, and without being anxious to write a liability insurance policy on it.

Nassim's point is that modern infrastructure, including bridges, inevitably leads to Black Swans. An overgrown tree in rural Ohio dislocated the lives of over 50 million people in the Northeast Blackout of 2003; no comparable event is conceivable when humans lived in dispersed tribes of hunter-gatherers. A single person harboring a newly-mutated virus could potentially infect the entire world in a few weeks today, something which was not true a century ago. The technologies that allow seven billion people to occupy the earth, most in reasonable security and comfort, are also used for wars that have the potential to end all those lives; those technologies are also complex, tightly-coupled, interconnected, and fragile. The speed of progress means that we have negligible empirical evidence on the long-term effects of modern diets, medical treatment, communication, education, or environmental impacts. This does not mean we should reject the modern world, kill 99.9% of the human race, and return to Neolithic technologies. It does mean we should be aware that we have created Black Swans. Weatherall is directionally correct. Yes, we should do better modeling. Yes, we should be aware of the weaknesses of modeling. But these things are no match for Black Swans.

However, Black Swans and bridges are not the biggest misunderstandings Weatherall has about Nassim Taleb's work. Next week we'll look at Weatherall, Taleb, option pricing, and fat tails.

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